SOLUTION: Sam and Allen applied for scholarships. The probability that Sam gets a scholarship is 0.91 and the probability that Allen gets a scholarship is 0.76. The probability they both d

Click here to see ALL problems on Probability-and-statistics

Question 188455: Sam and Allen applied for scholarships. The probability that Sam gets a scholarship is 0.91 and the probability that Allen gets a scholarship is 0.76. The probability they both do is 0.73.
What is the probability that Sam gets a scholarship but Allen doesn't?
What is the probability neither receives a scholarship?
If Sam receives one, what then is the conditional probability that Allen will also?
If Allen receives a scholarship, what then is the conditional probability that Same will not receive one?
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
1) P(S)*P(~A)=.91*.24=.2184.......P(~A)=1-.76=.24
:
2) P(neither) is 1-prob(both)=1-.73=.27
:
3)P (A|S)=P(S and A)/P(S)= .73/.91=.8022
:
4)P(~S|A)= P(~S and A)/P(A)=(.09)*(.76)/.76=.0684/.76=.09
:
P(~S and A)=.09*.76